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math.NT2026
On the Sum of a Prime and a Number that is not Square-Free
Ethan S. Lee, Rowan O'Clarey
We prove that every sufficiently large integer can be written as the sum of a prime and an integer that is not square-free. In addition, we expect this result holds for every $…
math.NT2025
On the sum of a prime and a square-free number co-prime to any integer with at most two prime factors
Ethan S. Lee, Rowan O'Clarey
Every natural number greater than can be written as the sum of a prime and a square-free number, and recent work has imposed additional divisibility conditions on the square-fr…